WordPress uses Name, email post fields to do post comments, If you renamed the your form elements name attributes to be f-name and f-email then your issue will be resolved. I have made changes in below code and it is working now.
<?php
if($_POST['f-submit']) {
if(!$_POST['f-name']) {
$error="<br>- Please enter your name";
}
if(!$_POST['f-email']) {
$error.="<br>- Please enter your email";
}
if(!$_POST['f-telephone']) {
$error.="<br>- Please enter your telephone number";
}
if(!$_POST['f-message']) {
$error.="<br>- Please enter your message";
}
if(!$_POST['f-checkbox']) {
$error.="<br>- Please confirm you agree to the Privacy Policy";
}
if ($error) {
$result="<div class="alert error">Whoops, there is an error. Please correct the following: ".$error.'</div>';
} else {
mail("[email protected]", "Contact Message", "Name: ".htmlspecialchars($_POST['f-name'])."
Email: ".htmlspecialchars($_POST['f-email'])."
Telephone: ".htmlspecialchars($_POST['f-telephone'])."
Company: ".htmlspecialchars($_POST['f-company'])."
Budget: ".htmlspecialchars($_POST['f-budget'])."
Message: ".htmlspecialchars($_POST['f-message']),
"From: [email protected]\r\n"
);
{
$_POST= array();
$result="<div class="alert thankyou" role="alert">THANK YOU! WE\"LL BE IN TOUCH SHORTLY...</div>';
}
$headers = "From: [email protected]\r\n";
}
}
?>
HTML
<form id="contactform" method="post" action="#section-2">
<?php echo $result; ?>
<div class="form-row-1 js-st">
<input id="name" type="text" name="f-name" placeholder="Name" value="<?php echo $_POST['f-name'];?>">
<input id="email" type="email" name="f-email" placeholder="Email Address" value="<?php echo $_POST['f-email'];?>">
</div>
<div class="form-row-2 js-st">
<input id="telno" type="text" name="f-telephone" placeholder="Telephone Number" value="<?php echo $_POST['f-telephone'];?>">
<input id="company" type="text" name="f-company" placeholder="Company [optional]" value="<?php echo $_POST['f-company'];?>">
</div>
<div class="form-row-3 js-st">
<textarea id="project-details" name="f-message" placeholder="Tell us about your project"><?php echo $_POST['f-message'];?></textarea>
</div>
<div class="form-row-4 js-st">
<input id="budget" type="text" name="f-budget" placeholder="Budget" value="<?php echo $_POST['f-budget'];?>">
<p class="budget-subline tl ">*We recommend putting in an approximate budget</p>
<input id="privacy-checkbox" type="checkbox" name="f-checkbox"><label id="privacy-label" for="privacy-checkbox">I agree to the <a href="https://wordpress.stackexchange.com/questions/360610/./privacy.php">privacy policy</a></label>
</div>
<input class="js-st" id="formsubmit" type="submit" name="f-submit" value="SUBMIT">
</form>